Sqrt(x)

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class Solution:
    def mySqrt(self, x: int) -> int:
        if x == 0:
            return 0
        first, last = 1, x
        while first <= last:
            mid = first + (last - first) // 2
            if mid == x // mid:
                return mid
            elif mid > x // mid:
                last = mid - 1
            else:
                first = mid + 1
        return last

Problem Classification

  1. Arithmetic Operations: The problem requires finding the square root of an integer, which is a fundamental arithmetic operation.

  2. Integer Manipulation: This problem deals specifically with integer values. It involves manipulating integers and understanding integer-specific operations, like integer division.

  3. Search Algorithms: The problem requires finding a specific value (the square root), and it employs a type of search algorithm (binary search) to efficiently find this value.

  4. Optimization Problem: At a broader level, this problem could be seen as an optimization problem, where you’re trying to find a specific value that satisfies certain conditions, and you’re trying to do so in the most efficient way possible.

Language Agnostic Coding Drills

The code is an implementation of an integer square root function, which finds the square root of a given integer ‘x’ and returns it as an integer. The code uses a binary search algorithm to efficiently find the square root.

Here’s a breakdown of this code into smaller units of learning that should be understood to comprehend the code:

  1. Variables and Data Types: The usage of variables is fundamental. In this code, variables are used to hold the input (x), the lower and upper bounds for the search (first, last), and the midpoint of the search range (mid).

  2. Conditional Statements (If and Else): Conditional statements are used to handle different cases: when ‘x’ equals to zero, when the midpoint is the square root, when the midpoint is too high, and when it is too low.

  3. Arithmetic Operations: Basic arithmetic operations are used here. The addition and division operations are used to compute the midpoint, and the comparison operations (equal, greater than, less than) are used to check the conditions.

  4. Loops (While Loop): A while loop is used here to continuously halve the search space until the square root is found. Understanding how a while loop works and how to control its condition is crucial.

  5. Functions and/or Methods: The code is written in a method of a class. Understanding how to define functions/methods, their inputs, and their outputs is important.

  6. Classes: Although not specifically required for this problem, understanding classes is helpful as the function is defined inside a class in this code.

Problem-Solving Approach:

  1. Understand the problem: The problem is to find the square root of an integer.

  2. Define the problem requirements: Given an integer ‘x’, find the square root as an integer.

  3. Break down the problem: The problem can be simplified into tasks:

    • If ‘x’ is 0, the square root is also 0.
    • Otherwise, start the search range from 1 to ‘x’.
    • Continuously halve the search space by comparing the midpoint squared with ‘x’ until the square root is found.

  4. Develop a solution: Pseudocode for the solution can be written as follows:

    • If ‘x’ is 0, return 0.
    • Define the search range as from 1 to ‘x’.
    • While the search range is valid:
      • Compute the midpoint.
      • If the midpoint squared is ‘x’, return the midpoint.
      • If the midpoint squared is greater than ‘x’, move the upper bound to the midpoint minus 1.
      • If the midpoint squared is less than ‘x’, move the lower bound to the midpoint plus 1.
    • Return the upper bound as the integer square root.

  5. Test the solution: The solution should be tested with various inputs to ensure that it handles all scenarios.

Targeted Drills in Python

  1. Variables and Data Types:
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# Integer
x = 10
print(x)

# Boolean
is_true = True
print(is_true)
  1. Conditional Statements (If and Else):
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x = 10
if x > 5:
    print("x is greater than 5")
else:
    print("x is not greater than 5")
  1. Arithmetic Operations:
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# Addition
sum = 5 + 5
print(sum)

# Division
div = 10 / 3
print(div)

# Integer Division
div_int = 10 // 3
print(div_int)

# Comparison
print(5 > 3)
  1. Loops (While Loop):
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i = 0
while i < 5:
    print(i)
    i += 1
  1. Functions and/or Methods:
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def say_hello(name):
    return "Hello, " + name

print(say_hello("World"))
  1. Classes:
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class Greeter:
    def __init__(self, name):
        self.name = name

    def greet(self):
        return "Hello, " + self.name

greeter = Greeter("World")
print(greeter.greet())

Problem Specific Drills:

This problem involves finding the square root using binary search. Let’s write a drill for binary search:

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def binary_search(array, target):
    first, last = 0, len(array) - 1
    while first <= last:
        mid = first + (last - first) // 2
        if array[mid] == target:
            return mid
        elif array[mid] > target:
            last = mid - 1
        else:
            first = mid + 1
    return -1  # Not found

numbers = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
print(binary_search(numbers, 7))

And a drill for finding the square root of a number:

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def square_root(x):
    return x ** 0.5

print(square_root(25))

Each of these drills helps build up the knowledge required to implement the final solution. To form the final solution, the drills would need to be adjusted and combined.